I think I will trisoup the floor and the ceiling, then use a few more bits of trisoup as needed on the walls. I forgot to say that the patches would be a guide for trisouping that would be deleted once the trisoup is finished.

Update: This is working very well. Trisouping the floor and the ceiling in a cave, then using a few more bits on the walls seems to be the correct approach. I am just winging it rather than tracing around patch meshes.